【Leetcode】1524. Number of Sub-arrays With Odd Sum

Subject address:

https://leetcode.com/problems/number-of-sub-arrays-with-odd-sum/

Given a length nnArray of$n$$A$ , ask the number of non-empty sub-arrays whose sum is odd. The result modulo$10^9+$Return after$7$ .

First find the prefix and the array $c[i]$即$c[i]={\sum }_{k=0}^{i-1}A\left[k\right]$ , and then use a hash table to record the number of even and odd prefix sums. Then traverse$A$ , Tohoku$When\; A\left[i\right]$ , if the prefix and$c[i+1]$ is an odd number, then look up$c[0:$How many even numbers are there in$i$$]$ , add them up, and get$A\left[i\right]$ is the number of sub-arrays whose sum of the right end point is an odd number; if the prefix and$c[i+1]$ is an even number and similarly. code show as below:

public class Solution {
    
    
    public int numOfSubarrays(int[] arr) {
    
    
        int MOD = (int) (1E9 + 7);
        // 为了加速，可以用数组代替哈希表，count[0]代表偶数个数，[1]代表奇数个数；
        // 空数组的前缀和是0，要计入
        int[] count = {
    
    1, 0};
        
        int res = 0;
        // 为了节省空间，不需要另外开数组算前缀和，可以直接用一个变量记录
        for (int i = 0, rem = 0; i < arr.length; i++) {
    
    
            rem = (rem + arr[i]) % 2;
            res = (res + count[rem ^ 1]) % MOD;
            count[rem]++;
        }
        
        return res;
    }
}

Time complexity $O\left(n\right)$ , space$O\left(1\right)$。